First question, and I suspect the answer is no - are the Zimbabwe - South Africa and JNB - LHR flights on the same PNR? If not, BA is entirely correct. They do not have to help your mother, you've accepted the risk by booking separate PNR's and they could leave it entirely up to you (or your insurance, but since you are US based, I expect you don't have any ) to sort it out. If it is on the same PNR, then it is entirely BA's problem, and they will have to provide options back for your mother.